LOSSLESS COMPRESSION AS A COMPLEXITY INDEX IN PALEOGEOBIOLOGY: ICHNOFABRICS AND STROMATOLITES AS TWO EXAMPLES

Quantifying qualitative indices in Earth sciences remains an issue. The adage “I know it when I see it” continues to be a part of Earth science because the structures we study are complex and not easily deconstructed into simpler parts. In information theory, the complexity of a digital file is equated to its information content, which, in turn, can be quantified via the use of lossless compression algorithms (e.g., gzip). Lossless compression algorithms reduce file size primarily by identifying and encoding redundant (i.e., regular) information. For example, a periodic sine wave would be highly redundant and therefore highly compressible, a completely random signal contains no event that can be predicted from earlier events and would be highly incompressible, and a “complex” system contains a mixture of the two and would have intermediate compressibility. Complexity analysis may find broad application in the Earth sciences where redundant and random processes interact. For example, ichnofabric index provides a qualitative way to determine the extent of bioturbation in sediments. In general, ichnofabric index is used to track the “complexity” of biogenic bed disruption (less disruption is less complex, more disruption is more complex). We have applied compression analysis to a variety of digital images displaying an ichnofabric index; our results parallel the qualitative index without the potential bias of the observer and open the possibility for finer resolution with respect to ichnofabric quantification. In another example, we have examined stromatolites and demonstrated a clear difference in compression between those considered predominantly “abiotic” (i.e., crystal fan microstructures) and those considered predominantly "biotic" (i.e., laminated microstructure) despite the fact that the structures appear similar to the human eye at the macroscopic scale. The difference likely results from the amount of random versus non-random processes inherent in the formation of each structure. Major compression differences are noted even at the macroscopic scale, such that analysis of this type might be used to examine the biogenicity of stromatolitic structures where microscopic analysis is not possible (e.g., the surface of Mars or other extraterrestrial locale).